With few exceptions, embryonic stem cells have only been grown from blastocyst-stage embryos. ES cell lines are conventionally isolated from the inner cell mass of blastocysts and in a few instances from cleavage stage embryos. There are several drawbacks to the techniques used to create these cells. From the perspective of the technique, the culturing of embryos to blastocysts occasionally has a relatively low success rate. Some people express the basic objection that embryonic stem (ES) cell research is rooted in the fact that ES-cell derivation deprives preimplantation-stage embryos of any further potential to develop into a complete human being. The following invention provides novel and unexpected methods of deriving embryonic stem cell lines and other embryo-derived cells for use in research and in medicine.